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1 BROOKHAVEN SCIENCE ASSOCIATES
13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
Smoothing Based on Best-fit Transformation
C. Yu
2 BROOKHAVEN SCIENCE ASSOCIATES
13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
Outline
• Introduction
• Principle
• Application in SSRF
• Application in NSLS-II
• More Consideration
• Conclusion
3 BROOKHAVEN SCIENCE ASSOCIATES
13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
What’s Smoothing
• a technique to achieve accurate relative
alignment of components
• a main concern of accelerator alignment
The reason for smoothing:
• limitation of survey control network
• slow floor movement
• tight relative alignment tolerance
• loose global alignment tolerance
Introduction
Smoothing techniques
• cubic spline functions (DESY)
• First Principle Component analysis (APS)
• Based on best fit transformation
4 BROOKHAVEN SCIENCE ASSOCIATES
13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
What’s best fit transformation
• Mathematically, take out the overall
translation or rotation between reference and
as-built coordinate systems
Smoothing Requirement
• Reference value of fiducials
• As-built value of fiducials
• Check the as-built location WRT reference
and can be realized by best fit transformation
Best Fit Transformation
Benefits
• Easy to understand
• Readily available in software
• Handily available with regard to reference
and as-built data
• And more
From Spatial Analyzer User Manual
3 translation, 3 rotation and 1 scale parameters
5 BROOKHAVEN SCIENCE ASSOCIATES
13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
How to use it for one set of girders or
magnet groups?
• Obtain reference data
• Obtain as-built data
• Perform best-fit transformation
• Compare the residuals of fiducials
• Decide if the beam orbit is smooth according
certain criteria.
What has been done by best-fit
transformation is taking out of the rotations
and translations of as-built values with
respect to global coordinate system and
showing the deviations relatively.
Repeat many times to check the whole
ring
Smoothing Based on Best Fit Transformation-Basics
Layout of C08G2 and C08G4 girder fiducials and best-
fit deviations of NSLS-II Storage ring
Comparison of C08G2 and C08G4 girder
fiducials before and after best-fit transformation.
6 BROOKHAVEN SCIENCE ASSOCIATES
13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
• In practice, 3 adjacent girders are used
• Overlap between cells is important. The number of best fit transformation equals to the number of
girders.
• It’s important to have accurate as-built survey data
• In order to describe the deviations clearly and make them easy to understand, local frames for each
girder should be established.
• The fiducials should be sorted in each group according to their location with respect to beam
• When a girder is determined to be adjusted, its upstream and downstream girders will be used to
transform the as-built survey data to reference data
• The method is not limited to circular accelerator.
Smoothing Based on Best Fit Transformation-More
7 BROOKHAVEN SCIENCE ASSOCIATES
13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
Application in SSRF (1)
• SSRF storage ring 432m
• Initial alignment 2007
• Re-alignment in 2012
• The best-fit transformation
based smoothing technique
was initialized.
• Sextupoles and quadrupoles
centers were used during best-
fit transformation process.
• Girders were rotated based on
the roll angle
• Multiple iterations (Realized by
MP of Spatial Analyzer) to
minimize the residuals
8 BROOKHAVEN SCIENCE ASSOCIATES
13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
Application in SSRF (2)
Computed adjusted amount in horizontal direction Computed adjusted amount in vertical direction
The good
• Circumference error >10 mm ignored.
• Most of the adjustment below 300 micron
• First attempt to apply this innovative idea,
alignment result was excellent
The bad
• 7 beam lines of phase 1 had to be re-
adjusted
9 BROOKHAVEN SCIENCE ASSOCIATES
13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
Application in NSLS-II (1)
• Storage ring ~791.5m
• Girder alignment for ~1 year
• No final survey before
commissioning
• Epoch 7 survey during shutdown
in May 2014 shows deviations of
components.
• Smoothing based on best fit
transformation of girder fiducials
were used.
10 BROOKHAVEN SCIENCE ASSOCIATES
13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
Application in NSLS-II (2)
Steps:
•Perform comprehensive survey for girder of
interested and its upstream and downstream ones.
•Compute the measured relative location of 3 girders.
•Perform a best-fitting between the measured and
reference coordinates to see if there are large
deviations. As a rule of thumb, the fitting RMS in both
X and Y direction should be below 0.05.
•If the fitting result is larger than 0.05, the downstream
fiducials of upstream girder and upsteam fiducials of
downstream girder will be used to establish girder
adjustment control network. The nominal coordinates
of those 4 fiducials will be used to best-fit and
transform the measured point group. The measured
point group will be used as survey control network and
the reference coordinates will be used as alignment
goal.
“DX Goal” and “DY Goal” shows the goal of
adjustment.
11 BROOKHAVEN SCIENCE ASSOCIATES
13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
Application in NSLS-II (3)
The fiducial deviations after best-fit transformation among all 3 adjacent girders.
Fiducial best-fit result
•Each fiducial will be shown 3 times
•RMS deviation in X and Y direction is 0.034
mm and 0.021 mm respectively
Work has been done
•22 girders which had been checked
•8 girders had been adjusted
•The maximum adjustment amount is below
300 micron.
12 BROOKHAVEN SCIENCE ASSOCIATES
13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
Application in NSLS-II (4)
The girder center deviations before and after smoothing.
Global deviation
•All girder centers WRT epoch 7 survey
•Still not a smooth curve, but relative girder
alignment is well within tolerance.
Nomenclature
•“O” means original survey
•“C” means it has been checked
•“A” means it has been aligned.
Lessons learned
•Girders should be checked in a consecutive manner
13 BROOKHAVEN SCIENCE ASSOCIATES
13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
Discussions
• The best-fit transformation based smoothing technique is easy to understand and use
• Its application is successful for the partial alignment of NSLS-II project.
• It also yielded excellent alignment quality when it was applied in SSRF for a whole
machine re-adjustment during 2012 shutdown.
• The best-fit transformation based smoothing technique can tackle beamline alignment
constraints by avoid moving girders around straight section unless it’s absolutely
necessary.
• By surveying and adjusting the storage ring cell by cell, good storage ring alignment can
be maintained. This is important for a new machine as no major shutdown will be
necessary at the early stage of running due to large floor settlement.
14 BROOKHAVEN SCIENCE ASSOCIATES
13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
Summary
• Best-fit transformation is a basic technique for accelerator alignment in the current time,
but smoothing seems a little bit fancy as it usually associates with different language,
such as Fourier function, cubic spline or Principal Curve Analysis etc. But the application
of best-fit transformation makes smoothing a lot easier and any surveyor can do it.
• It’s not only a great tool for partial and whole alignment of an accelerator at the beginning
of running a machine, but also a possible solution for long term maintenance of storage
ring when more constraints present.
• With dedicated script, the whole smoothing process can be fully automated and high
efficiency is expected.
15 BROOKHAVEN SCIENCE ASSOCIATES
13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
Acknowledgment
The author would like to thank all the staff who involved in the
NSLS-II and SSRF alignment activities.
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13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China
Thanks for your attention!